How can I stop my shower doors from hitting one another and making an awful noise?

Hard to tell. I would slowly operate the doors a few times and try to see where something might be contacting another piece. I don't think the top brackets are touching each other unless somehow the screws had losened. The top rail should keep the apart.

The spacer on the bottom I think might be the issue. The outside door looks pretty low. The top rail might have sagged a little or was not installed level and the outside door might be hitting it as it passed over it. Or possibly some sort of deposits have built up on the bottom.

You should be able to raise the outside door by removing it and repositioning the screws in the bracket. It differs by model but I haven't seen a set of doors that don't have some adjustment. When the doors are removed also make sure that bottom plastic spacer is clean and properly installed.

If you do this, wear shoes, a long sleeve shirt, gloves and safety glasses in case the glass breaks.

It looks like the inside door is not completely in the track. It's possible that the wheels are worn out and therefore allowing the tops of the door to come closer together than they should.

It also looks like the top rail might be bent down. Measure the height of the opening at each end and also the middle. If the middle is lower than the ends, some careful bending might be in order.